There are plenty of applications and analysis for time-independent elliptic partial differential equations in the literature hinting at the benefits of overtesting by using more collocation conditions than the number of basis functions. Overtesting not only reduces the problem size, but is also known to be necessary for stability and convergence of widely used unsymmetric Kansa-type strong-form collocation methods. We consider kernel-based meshfree methods, which is a method of lines with collocation and overtesting spatially, for solving parabolic partial differential equations on surfaces without parametrization. In this paper, we extend the time-independent convergence theories for overtesting techniques to the parabolic equations on smooth and closed surfaces.

翻译：文献中关于时间无关椭圆型偏微分方程的大量应用与分析表明，通过使用比基函数数量更多的配点条件进行过测试具有优势。过测试不仅能减小问题规模，而且对于广泛使用的非对称Kansa型强形式配点法的稳定性和收敛性而言也是必要的。我们考虑基于核的无网格方法（一种在空间上结合配点与过测试的线法），用于求解无参数化处理曲面上的抛物型偏微分方程。本文中，我们将过测试技术的时间无关收敛理论推广到光滑闭合曲面上的抛物型方程。